Resumen de Pointwise convergence of fractional powers of Hermite type operators

Guillermo Flores, Gustavo Garrigós, Teresa María Signes Signes, Beatriz Viviani

• When L is the Hermite or the Ornstein–Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function f so that the fractional power Lσf(x0) is well-defined at a given point x0. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators (−∆ + R) σ, with R > 0.